It was proposed recently that type IIB orientifold compactifications on CY(3) in the presence of fluxes exhibit an attractor mechanism similar to the one in black hole physics, in other words that minimizing the relevant scalar potential is equivalent to solving a system of attractor equations. So far this conjecture has been verified only numerically. We show by analytical means that the conjectured susy attractor equations do indeed give supersymmetric minima of the relevant scalar potential.

Theories unifying gravity with other interactions suggest temporal and spatial variation of the fundamental \'constants\' in expanding Universe. The spatial variation can explain fine tuning of the fundamental constants which allows humans (and any life) to appear. We appeared in the area of the Universe where the values of the fundamental constants are consistent with our existence. I present a review of works devoted to the variation of the fine structure constant alpha, strong interaction and fundamental masses (Higgs vacuum).

The Fermilab Tevatron is currently the highest energy particle collider in the world and is host of the CDF and DZero experiments. Measurements performed by these two international collaborations have significantly improved our knowledge of subatomic physics and helped further constrain different scenarios of physics beyond the Standard Model. A summary of some of the latest results and future experimental goals of the Tevatron\'s experiments will be presented.

Inflation is generically a never ending process, with new \'pocket universes\' constantly being formed. All possible events will happen an infinite number of times in such an eternally inflating universe. Unless we learn how to compare these infinities, we will not be able to make any predictions at all. I will discuss some proposed approaches to this \'measure problem\'.